Stylesheets are one of the easiest ways to produce problems with different browsers. Taking a step like the one you suggest would rapidly result in a site that was only navigatible in recent versions of IE.

I understand the proposal like this: When you _browse_ the site, it serves you a link to your style sheet.

If you have a personal style sheet, it doesn't matter if it will break "different browsers". On person, one browser, one style sheet.